Predictive Soave-Redlich-Kwong Equation of State (PSRK)

Dr. K. Fischer, Dr. S. Horstmann, Dipl.-Chem. H. Gardeler


The application of so-called gE-mixing rules shows different advantages compared to classical mixing rules, which can only be used for nonpolar or slightly polar compounds. In PSRK the cubic Soave-Redlich-Kwong equation of state [1] is combined with the UNIFAC model [2], whereby the pure component parameters bi and aii are obtained from critical data and vapor pressure data using the Mathias-Copeman expression [3] or the generalized form concerning the acentric factor.

Status and Results

Using the PSRK equation of state phase equilibria for systems with subcritical and supercritical compounds can be predicted by using only pure component properties (Tcr,i, Pcr,i, w) and group interaction parameters. The original UNIFAC parameters can be used directly. Parameters for nineteen new main groups (NH3, CO2, CH4, O2, Ar, N2, H2S, H2, CO, SO2, NO, N2O, SF6, He, Ne, Kr, Xe, HCl, HBr) have been fitted using phase equilibrium information from the Dortmund Data Bank (VLE of low boiling substances and gas solubilities). Fig. 1 shows the current status of the PSRK group interaction parameter table.


Fig. 1 Current status of the PSRK method (
Download a more detailed view of the PSRK-Matrix  (47K))


PSRK has all the advantages of an equation of state. It can be applied to systems with supercritical components and allows the calculation of densities, enthalpies and other properties even in systems with polar components. In Fig. 2 and Fig. 3 results of the PSRK model are shown. More results have been published [4-10].


Fig. 2 VLE of the binary system Acetone (1) - Water (2), (· ,o) experimental data, (¾) PSRK


FigFig. 3 VLE of the binary system CO2 (1) - CH3CCl3 (2)

Latest efforts enabled the prediction of high asymmetric systems by introducing an empirical expression to correct the van der Waals properties of the hydrocarbon group as used in the UNIFAC model [11]. Fig. 4 shows the improvements on the example CH4 (1) - n-hexadecane (2).


Fig. 4 VLE of the binary system CH4 (1) - n-hexadecane (2), (- - -) PSRK (original van der Waals properties), (¾ ¾ ) PSRK (effective van der Waals properties)

Another application of PSRK is the prediction of critical lines of mixtures. Fig. 5 shows the vapor-liquid equilibrium of the system CO2 (1) - Ethane (2) also including azeotropic points and critical data. Especially in the case that there are no or only few high pressure VLE data available critical data can be used to improve the PSRK group interaction parameters. For this reason a database for critical data of mixtures and an apparatus for the measurement of critical points of pure components and mixtures were developed.


Fig. 5 VLE, azeotropic points and critical data of the binary system CO2 (1) - Ethane (2)

In the future the PSRK parameter matrix and the required VLE data base will be constantly updated. The PSRK model has been integrated in most commercial process simulators.


The authors thank the Arbeitsgemeinschaft Industrieller Forschungsvereinigungen (AIF) for financial support.


  1. G. Soave, Chem. Eng. Sci. 27, 1197 (1972)
  2. H. K. Hansen, P. Rasmussen, Aa. Fredenslund, M. Schiller, J. Gmehling, Ind. Eng. Chem. Res. 30, 2352 (1991)
  3. P. M. Mathias, T.W. Copeman, Fluid Phase Equilibria 13, 91 (1983)
  4. T. Holderbaum, J. Gmehling, Fluid Phase Equilibria 70, 251 (1991)
  5. T. Holderbaum, J. Gmehling, Chem.Ing.Tech. 63, 57 (1991)
  6. T. Holderbaum, VDI Fortschrittsberichte, Reihe 3, Nr. 243, VDI-Verlag, Düsseldorf 1991
  7. K. Fischer, VDI Fortschrittsberichte, Reihe 3, Nr. 324, VDI-Verlag, Düsseldorf 1993
  8. K. Fischer, J. Gmehling, Further development, status and results of the PSRK method for the prediction of vapor-liquid equilibria and gas solubilities, Fluid Phase Equilibria 121, 185 (1996)
  9. J. Gmehling, Jiding Li, K. Fischer, Further Development of the PSRK Model for the Prediction of Gas Solubilities and Vapor-Liquid Equilibria at Low and High Pressures II, Fluid Phase Equilibria 141, 113-127 (1997)
  10. J. Gmehling, Present status of group-contribution methods for the synthesis and design of chemical processes, Fluid Phase Equilibria 144, 37-47 (1998)
  11. Jiding Li, K. Fischer, J. Gmehling, Prediction of Vapor-Liquid Equilibria for Asymmetric Systems at Low and High Pressures with the PSRK Model, Fluid Phase Equilibria 143, 71-82 (1998) 

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